This invention relates to digital filters, particularly to tunable digital filters having low noise characteristics for use in digital signal processing.
There are several particularly important factors that affect the design of tunable digital filters for digital signal processing. First, it is important to minimize the introduction of truncation noise, sometimes also called "round-off" noise. This kind of noise is introduced as a result of truncating the least significant digits of a digital word in order to fit the word within an available register. Second, the filter must not experience limit cycles as a result of overflow errors, i.e., it must not oscillate. Third, in order for the filter to be practical as a tunable filter, the filter coefficients must be rapidly calculable. Prior art digital filters of second or higher order have lacked this combination of features.
One commonly known topology for a digital filter is the "direct form" filter. In this topology, the coefficients of the filter structure are exactly the same as the coefficients of the z-domain transfer function. The coefficients of the direct form filter are relatively easy to calculate, but the filter suffers from significant introduction of truncation noise, particularly at low frequencies. In addition, the direct form digital filter can experience limit cycles unless special care is taken to avoid the conditions that cause overflow errors. A description of the direct form filter can be found in R. Roberts and C. Mullis, Digital Signal Processing (Addison-Wesley, 1987). pp. 72-74. TK 5102.5R525.
Another previously known digital filter topology is the "normal form" filter. In this topology, instead of acting directly on the input signal, the filter acts on state variables derived from the input signal, and the filter structure corresponds to a state space model of the filter. Although the normal form filter provides much better low-frequency noise characteristics than the direct form filter and cannot experience limit cycles, its coefficients are difficult and time-consuming to calculate. In addition, the normal form filter coefficients can exceed 2 in value, which makes implementation of the filter in fixed-point digital signal processing hardware difficult by requiring scaling operations. A description of the normal form filter can be found in Digital Signal Processing, id at pp 396-98.
Accordingly, it can be seen that there has been a need for a digital filter topology that produces less truncation noise, cannot experience limit cycles due to overflow errors, and permits rapid computation of the filter coefficients so that the filter can be tuned in real time.